A number of appliances have been proposed to assist the control of urine flow in men whose urinary sphincter muscles may have become weakened or in whom the associated nerves may have been damaged, resulting in involuntary flow of the urine, from small leakage to significant flow. The non-surgical external appliances have included, e.g., penis clamps which apply a closing pressure to the portion of the urethra that extends through the penis. These devices can be uncomfortable for the wearer, and require manipulation to release the external pressure so that the wearer can void his bladder. Also, the wearing of this type of aid can result in necrosis of tissues around the area where the penis clamp is worn and can result in urinary tract infections if worn for extended durations. An alternative incontinence aid is described in Vincent U.S. Pat. No. 3,080,865. That device involves an inflatable balloon that is to be worn on a spring member so that the balloon applies some pressure against the patient's perineum. However the device is cumbersome, and is difficult to install and remove. Another alternative incontinence aid is described in Kiser U.S. Pat. No. 5,727,568, involving a rigid block that is pressed against a narrow portion of the patient's penis to apply closing pressure to the urethra without applying pressure to other tissues. The device can be uncomfortable to wear and has to be custom made to fit the individual patient. The device requires straps that pass in the front of the patient's lower abdomen to hold the rigid pressure block, and the patient's penis, at a fixed location. Some patients require special underwear to hold the device properly in place.